In the deformation of a material, for example, in press forming of a plate material, it has been known that a forming crack occurs in a formed product if a forming condition is not appropriate. Therefore, there has been used a method in which, by using a computer, the press forming of the plate material is simulated under various forming conditions and validity of the forming conditions is determined based on the result (for example, Patent Literature 1).
In general, such a method repeatedly executes the following three steps until an appropriate forming condition under which no forming crack occurs and also other requirements (for example, weight reduction, thinning, and so on of a product) are satisfied is obtained:
(1) The press forming is simulated under a set forming condition and strains of portions of a material are successively calculated by using the simulation result;
(2) Determination is made regarding the occurrence of a forming crack based on whether or not the calculated strain exceeds FLC (Forming Limit Curve) depicted in FLD (Forming Limit Diagram) prepared in advance for each material; and
(3) When it is determined that the forming crack occurs, a forming condition of a portion thought to be a cause of the occurrence of the forming crack is corrected.
Such a method of searching for the appropriate forming condition by the simulation of the press forming with reference to the forming limit diagram is very useful for reducing the cost at a product design stage and shortening a design period.
However, the conventional method determines whether or not the forming crack occurs, simply by referring to the forming limit diagram (proportional deformation FLD) in a case of what is called proportional deformation whose strain direction is always constant, and even if applied to actual press forming accompanied by complicated deformation, the method is not often able to find the appropriate forming condition. In other words, the conventional method is greatly deformation path-dependent and is not applicable to a phenomenon such as a collision causing complicated deformation.
Therefore, in recent years, a method of determining whether or not a forming crack occurs by using a stress (stress FLD) instead of the strain has been developed. For example, Patent Literature 2 discloses a method of estimating a fracture limit curve of a strain space in a proportional load path, converting the fracture limit curve of the strain space to a fracture limit curve of a stress space (fracture limit stress curve), calculating fracture risk by using the fracture limit stress curve, and performing fracture determination based on the calculated fracture risk. Such a method is capable of performing the fracture determination regarding a fracture determination target portion in a process including one deformation path change or more. In other words, such a method is less dependent on the deformation path and is also applicable to a phenomenon such as a collision causing complicated deformation.
Incidentally, in the conventional method, when a fracture occurs in a certain element, a fracture state is expressed by eliminating this element. When some element is eliminated, a stress having been applied to the element is dispersedly applied to elements therearound. Therefore, if the size of the eliminated element is small, the stress applied to its surroundings is also small and a crack gradually progresses, but when the size of the eliminated element is large, the stress applied to elements therearound is large and a crack in the simulation is likely to progress more than actually. Therefore, in the conventional method, it is sometimes difficult to predict a behavior after the occurrence of the fracture.
For example, Patent Literature 3 discloses a method in which, in a collision analysis device which models, by a finite element method, a shock absorber composed of a set of cylindrical bodies whose axes are set parallel to one another, causes the shock absorber to collide with a collision target modeled by a finite element method in a predetermined manner, and analyzes the collision, a correction characteristic is set so as to suppress an increase of a stress in a region where the total drag characteristic expressed by a relation between a stress and a strain at the time of the compression of the modeled shock absorber exceeds a preset strain value. More concretely, it discloses a correction characteristic in which a stress σ decreases in accordance with an increase of a strain ε in a region where the strain ε exceeds ε1. Such a method is capable of naturally and accurately reproducing and analyzing a collision in a wide characteristic range of stress-strain control.
However, Patent Literature 3 does not disclose a concrete way of setting the correction characteristic.